This paper presents three-photon absorption (3PA) measurement results for nine direct-gap semiconductors, including full 3PA spectra for ZnSe, ZnS, and GaAs. These results, along with our theory of 3PA using an 8-band Kane model (4 bands with double spin degeneracy), help to explain the significant disagreements between experiments and theory in the literature to date. 3PA in the 8-band model exhibits quantum interference between the various possible pathways that is not observed in previous 2-band theories. We present measurements of degenerate 3PA coefficients in InSb, GaAs, CdTe, CdSe, ZnTe, CdS, ZnSe, ZnO, and ZnS. We examine bandgap, 𝐸 𝑔 , scaling using 2-band tunneling and perturbation theories that show agreement with the predicted 𝐸 𝑔 −7 dependence; however, For those semiconductors for which we measured full 3PA spectra, we observe significant discrepancies with both 2-band theories. On the other hand, our 8-band model shows excellent agreement with the spectral data. We then use our 8-band theory to predict the 3PA spectra for 15 different semiconductors in their zincblende form. These results allow prediction and interpretation of the 3PA coefficients for various narrow to wide bandgap semiconductors.
Statistical graphics is, or should be, an transdisciplinary field informed by scientific, statistical, computing, aesthetic, psychological and sociological considerations. The sciences (natural, applied or social and indeed also various literary, linguistic and historical disciplines) generate data relevant to various problems that are amenable to graphical display. Statistics advises or instructs on what should be plotted. Software and hardware are needed to produce displays in practice: very few would now reach for their pens and graph paper as was still common even some twenty or thirty years ago. We clearly should ponder how far graphics are attractive or not, and especially how far graphics work or not, in terms of being interpreted appropriately by users. But sociological considerations also? I suggest that a full appreciation of the situation of graphics within statistical science depends on recognising and trying to explain a variety of attitudes and behaviours. 'Statistical science' is understood here to range from the science of statistics to any part of science done statistically. Graphics is prominent in almost every introductory course or text and central to a large part of statistical practice. Indeed, I regularly attend scientific presentations largely innocent of p values, t statistics, confidence intervals or even figures of merit such as R 2 or AIC, but which include curve or model fits kept honest, mostly, by intense graphical analysis, large datasets and attention to the underlying science.
We present femtosecond pump-probe measurements of the nondegenerate (1960 nm excitation and 1176-1326 nm probe) two-photon absorption spectra of 8 nm GaAs/12 nm Al0.32Ga0.68As quantum well waveguides. Experiments were performed with light pulses co-polarized normal and tangential to the quantum well plane. The results are compared to perturbative calculations of transition rates between states determined by the k · p method with an 8 or 14 band basis. We find excellent agreement between theory and experiment for normal polarization, then use the model to support predictions of orders-of-magnitude enhancement of nondegenerate two-photon absorption as one constituent photon energy nears an intersubband resonance.
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